Flexural Vibration of Atomic Force Microscope Cantilever with Dimensional Effects

Document Type : Research Article



Atomic Force microscope (AFM) is one of the powerful and useful tools in nanoscale science and
technologies with applications from surface characterization in material science, to the study of living
biological systems in their natural environment. AFM operate in three modes of contact, non-contact and
tapping mode. In this paper, by focusing on the development of a more comprehensive model of an AFM
micro-cantilever beam, considering the effects of mass and rotary inertia of the tip using Euler-Bernoulli
beam theory is considered. The comparison of the present results and the results of other investigators, which
has been done in case studies, generally shows a very good agreement. The results show that the effect of
mass and rotary inertia of the tip depending on its dimensions is important and should be considered. Finally,
the effects of cantilever inclination and tip height on the resonance frequencies are also examined.


[1] Binnig G.; Quate C. F.; Gerber C.; “Atomic Force Microscope”, Phys. Rev. Lett., vol. 56, p.p. 930-933, 1986.
[2] Tortonese M.; Barrett R. C.; Quate C. F.; “Atomic Resolution with an Atomic Microscope Using Piezoresistive Detection”, Appl. Phys. Lett., Vol. 62, p.p. 834–836, 1993.
[3] Giessibl F. J.; “High-Speed Force Sensor for Force Microscopy and Profilometry Utilizing a Quartz Tuning Fork”, Appl. Phys. Lett., vol 73, p.p. 3956–3958, 1998.
[4] Rogers B.; York D.; hisman N.; Jones M.; Murray K.;.; “Tapping Mode Atomic Force Microscopy in Liquid with an Insulated Piezoelectricmicro-Actuator”, Rev. Sci. Instrum., vol. 73, p.p. 3242–3244, 2002.
[5] Lin S.; Chen J. L.; Huang. L. S; Lin H. W.; “Measurements of the Forces in Protein Interactions with Atomic Force Microscopy”, J. Current Proteomics, vol. 2, p.p. 55-81, 2005.
[6] Bradbury S.; Bracegirdle B.; Introduction to Light Microscopy, Royal Microscopical Society Handbook, Number 42, Oxford Press, 1998.
[7] Hohmura K. I.; Itokazu Y.; Yoshimura S. H.; Mizuguchi G.; Masamura Y.; Takeyasu K.; Shiomi Y.; Tsurimoto T.; “Atomic Force Microscopy with Carbon Nanotube Probe Resolves the Subunit Organization of Protein Complexes”, J. of Electron Microscopy, vol. 74, p.p. 4061-4068, 2000.
[8] Colton R. J.; “Nanoscale Measurement and Manipulation”, J. Vac. Sci. Technol. B, vol. 22, p.p. 1-11, 2004.
[9] Jalili N.; Dadfarnia M.; Dawson D. M.; “A Fresh Insight into the Microcantilever-sample Interaction Problem in Non-contact Atomic Force Microscopy”, ASME J. Dyn. Syst., Meas.,Control., vol. 126, p.p. 327-335, 2004.
[10] Turner J. A.; Hirsekorn S.; Rabe U; Arnold W.; “High-Frequency of Atomic-force Microscope Cantilevers”, J. Appl. Phys., vol. 82, p.p. 967-979, 1997.
[11] Turner J. A.; Wiehn J. S.; “Sensitivity of Flexural and Torsional Vibration Modes of Atomic Force Microscope Cantilevers to Surface Stiffness Variations”, J. Nanotechnology, vol. 12, p.p. 322-330, 2001.
[12] Chang W. J.; “Sensitivity of Vibration Modes of Atomic Force Microscope Cantilevers in Continuous Surface Contact”, Nanotechnology, vol. 13, p.p. 510-514, 2002.
[13] Rabe U.; Turner J. A.; and Arnold W.; “Analysis of the Frequency Response of Atomic Force Microscope Cantilevers”, J. Appl. Phys. A, vol. 66,p.p. 277–282, 1998.
[14] Mahdavi M. H.; Farshidianfar A.; Dalir H.; “High Frequency Analysis of a Non-contact Atomic Force Microscopy Microcantilever”, Proc. of Int. Conf. on Mechanical Engineering Conference, Isfahan, Iran, 2006.
[15] Stokey W. F.; Vibration of Systems Having Distributed Mass and Elasticity, in Shock and Vibration Handbook, 5th Edition. by Harris C. M. and Piersol A. G.; McGraw-Hill, 2002.
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